Trigonometry

Problem 101

21. Find the coterminal of 60

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Problem 102

The sliding board as shown is 15 feet long and meets the ground at a 4040^{\circ} angle. What is the height of the ladder to the nearest tenth? \begin{tabular}{|l|} \hline sin400.6428\sin 40^{\circ} \approx 0.6428 \\ \hline cos400.7660\cos 40^{\circ} \approx 0.7660 \\ \hline \end{tabular} 23.3 ft 9.6 ft 19.6 ft 11.5 ft

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Problem 103

Let (3,2)(-3,-2) be a point on the terminal side of θ\theta. Find the exact values of sinθ,secθ\sin \theta, \sec \theta, and tanθ\tan \theta. \square

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Problem 104

Find all solutions of the equation in the interval [0,2π)[0,2 \pi). 2cosθ2=02 \cos \theta-\sqrt{2}=0
Write your answer in radians in terms of π\pi. If there is more than one solution, separate them with commas. θ=\theta= \square

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Problem 105

2. Del gráfico mostrado, halla ab\mathrm{a}-\mathrm{b}.

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Problem 106

3. Si el punto (π3;2n12n+1)\left(\frac{\pi}{3} ; \frac{2 n-1}{2 n+1}\right) pertenece a la gráfica de la función y=cosxy=\cos x, demuestra que n=3/2n=3 / 2

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Problem 107

sin2xsinx=0\sin 2 x-\sin x=0

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Problem 108

sinθ(1+tanθ)+cosθ(1+cotθ)=(secθ+cosecθ)\begin{array}{l}\sin \theta(1+\tan \theta)+\cos \theta \quad(1+\cot \theta) \\ \qquad=(\sec \theta+\operatorname{cosec} \theta)\end{array}

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Problem 109

1+cot2θ1+cosecθ=cosecθ\frac{1+\cot ^{2} \theta}{1+\operatorname{cosec} \theta}=\operatorname{cosec} \theta

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Problem 110

What is the Y component of vector A if the magnitude of A is 12.8 and the angle θ\theta is 38

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Problem 111

Fill in the blank. Let θ\theta be an angle in standard position with (x,y)(x, y) a point on the terminal side of θ\theta and r=x2+y20r=\sqrt{x^{2}+y^{2}} \neq 0. sin(θ)=\sin (\theta)= \square

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Problem 112

The point is on the terminal side of an angle in standard position. Find the exact values of the six trigonometric functions of the angle. (312,215)sinθ=cosθ=tanθ=cscθ=secθ=cotθ=\begin{array}{l} \left(3 \frac{1}{2},-2 \sqrt{15}\right) \\ \sin \theta=\square \\ \cos \theta=\square \\ \tan \theta=\square \\ \csc \theta=\square \\ \sec \theta=\square \\ \cot \theta=\square \end{array}

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Problem 113

Solve for xx where xϵ[0,2π],,,2cos2x+cosx=1x \epsilon[0,2 \pi],,, 2 \cos ^{2} x+\cos x=1 :Select one x=π/6,5π/6,π/2x=\pi / 6,5 \pi / 6, \pi / 2 non of them x=π/3,π,5π/3x=π/6,5π/6,3π/2\begin{array}{r} x=\pi / 3, \pi, 5 \pi / 3 \\ x=\pi / 6,5 \pi / 6,3 \pi / 2 \end{array}

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Problem 114

Axample 4 : In a right triangle ABCA B C, right-angled at BB, if tanA=1\tan A=1, then verify that 2sinAcosA=12 \sin \mathrm{A} \cos \mathrm{A}=1

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Problem 115

12) XYZX Y Z is a right-angled triangle at YY, if YZ=2XYY Z=2 X Y Find the value of each of :tanZ,tanX,cosZ,cos: \tan Z, \tan X, \cos Z, \cos

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Problem 116

Question Express sinC\sin C as a fraction in simplest terms.
Answer Attempt 2 out of 2 sinC=\sin C= \square Submit Answer \sqrt{ } MacBook Air

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Problem 117

Determine the interval(s) on which the function f(x)=cscxf(x)=\csc x is continuous, then analyze the limits limxπ/4f(x)\lim _{x \rightarrow-\pi / 4} f(x) and limx2πf(x)\lim _{x \rightarrow 2 \pi^{-}} f(x).

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Problem 118

Question
Express cosH\cos H as a fraction in simplest terms.
Answer Attempt 1 out of 2 cosH=\cos H= \square Submit Answer \sqrt{ } Coppright Cz0244 DellaMathoom Al Rights Reserved. Privacy Pollicy | Terms of Service MacBook Air

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Problem 119

Refer to right triangle ABCA B C with C=90C=90^{\circ} as shown in the figure (not drawn to scale). Solve for all remaining parts using the given information. Round side lengths to the nearest hundredth of a foot and angle measures to the nearest hundredth of a degree. b=18.26ft,c=21.50ftb=18.26 \mathrm{ft}, c=21.50 \mathrm{ft} a=11.33b=\begin{array}{l} a=11.33 \\ b= \end{array} \square c=c= \qquad A=31.73B=58.27\begin{array}{l} A=31.73 \\ B=58.27 \end{array}

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Problem 120

Listen The Period of both y=sinxy=\sin x and y=cosxy=\cos x is π\pi. True False Submit Quiz 4 of 5 questions saved MacBook Pro

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Problem 121

=3+2cotθ=3+2 \cot \theta
3. Simplify sinθ(sinθ+cosθcotθ)\sin \theta(\sin \theta+\cos \theta \cot \theta)

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Problem 122

(38) Draw the graph of y=2sin1xπyπy=2 \sin ^{-1} x \quad-\pi \leq y \leq \pi

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Problem 123

(h) 1cosecθcotθ=cosecθ+cotθ\frac{1}{\operatorname{cosec} \theta-\cot \theta}=\operatorname{cosec} \theta+\cot \theta (i) sinθ+cosθsecθ+cosecθ=sinθcosθ\frac{\sin \theta+\cos \theta}{\sec \theta+\operatorname{cosec} \theta}=\sin \theta \cdot \cos \theta (j) tanθ+tanαcotθ+cotα=tanαtanθ\frac{\tan \theta+\tan \alpha}{\cot \theta+\cot \alpha}=\tan \alpha \cdot \tan \theta

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Problem 124

What is cot(3π4)\cot \left(-\frac{3 \pi}{4}\right) ? [?][?]

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Problem 125

Find α\alpha in degrees. α=\alpha= \square Round to the nearest hundredth.

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Problem 126

If triangle ABCA B C has A=52\angle A=52^{\circ}, side a=178a=178, and side b=234b=234, then which of the following is true? A. B=62.3\angle B=62.3^{\circ} B. There is no solution. C. B=62.3\angle B=62.3^{\circ} or 117.7117.7^{\circ} D. B=117.7\angle B=117.7^{\circ}

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Problem 127

Note: Triangle may not be drawn to scale. Suppose a=10\mathrm{a}=10 and c=11\mathrm{c}=11. Round answers to one decimal place: sin(A)=cos(A)=tan(A)=sec(A)=csc(A)=cot(A)=\begin{array}{l} \sin (A)=\square \\ \cos (A)=\square \\ \tan (A)=\square \\ \sec (A)=\square \\ \csc (A)=\square \\ \cot (A)=\square \end{array}

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Problem 128

2. For the following, solve the trigonometric equations on the interval 0θ2π0 \leq \theta \leq 2 \pi. a. 2cosθ+1=02 \cos \theta+1=0 b. tan2θ=1\tan ^{2} \theta=1 c. 2sin2θ1=02 \sin ^{2} \theta-1=0

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Problem 129

(1) y=3cos(π30x)+8y=3 \cos \left(\frac{\pi}{30} x\right)+8 (3) y=3cos(π30x)+8y=-3 \cos \left(\frac{\pi}{30} x\right)+8 (2) y=3cos(π15x)+5y=3 \cos \left(\frac{\pi}{15} x\right)+5 (4) y=3cos(π15x)+5y=-3 \cos \left(\frac{\pi}{15} x\right)+5

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Problem 130

(h) 1cosecθcotθ=cosecθ+cotθ\frac{1}{\operatorname{cosec} \theta-\cot \theta}=\operatorname{cosec} \theta+\cot \theta (i) sinθ+cosθsecθ+cosecθ=sinθcosθ\frac{\sin \theta+\cos \theta}{\sec \theta+\operatorname{cosec} \theta}=\sin \theta \cdot \cos \theta (j) tanθ+tanαcotθ+cotα=tanαtanθ\frac{\tan \theta+\tan \alpha}{\cot \theta+\cot \alpha}=\tan \alpha \cdot \tan \theta

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Problem 131

3. Each of the following graphs is of the form y=Asin(Bx)+Cy=A \sin (B * x)+C or y=Acos(Bx)+Cy=A \cos (B x)+C where B>0B>0. Write the equation of the graph for each of them. a. b. c.

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Problem 132

Draw the following graph on the interval 330<x<30-330^{\circ}<x<30^{\circ} : y=3cos(x75)y=-3 \cos \left(x-75^{\circ}\right)
Clear All Draw: MM

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Problem 133

If sin(θ)=57\sin (\theta)=-\frac{5}{7} and θ\theta is in the 4 th quadrant, find th If the value doesn't exist, type DNE. cos(θ)=csc(θ)=sec(θ)=tan(θ)=cot(θ)=\begin{array}{l} \cos (\theta)=\square \\ \csc (\theta)=\square \\ \sec (\theta)=\square \\ \tan (\theta)=\square \\ \cot (\theta)=\square \end{array}

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Problem 134

If cos(θ)=19\cos (\theta)=\frac{1}{9} and θ\theta is in the 4th quadrant, find the following: If the value doesn't exist, type DNE. sin(θ)=csc(θ)=sec(θ)=tan(θ)=cot(θ)=\begin{array}{l} \sin (\theta)=\square \\ \csc (\theta)=\square \\ \sec (\theta)=\square \\ \tan (\theta)=\square \\ \cot (\theta)=\square \end{array} Message instructor Post to forum

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Problem 135

A right triangle has side lengths 8,15 , and 17 as shown below. Use these lengths to find tanA,sinA\tan A, \sin A, and cosA\cos A. tanA=sinA=cosA=\begin{array}{l} \tan A= \\ \sin A= \\ \cos A= \end{array} \square \square

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Problem 136

Evaluate sec1(2)\sec ^{-1}(-\sqrt{2}). Enter an exact answer in radians.
Provide your answer below: sec1(2)=\sec ^{-1}(-\sqrt{2})= \square rad

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Problem 137

Find the exact value of the expression. sec[sin1(2107)]\sec \left[\sin ^{-1}\left(\frac{2 \sqrt{10}}{7}\right)\right]
Select the correct choice and fill in any answer boxes in your choice below. A. sec[sin1(2107)]=\sec \left[\sin ^{-1}\left(\frac{2 \sqrt{10}}{7}\right)\right]= \square (Simplify your answer, including any radicals. Use integers or fractions for any number B. There is no solution.

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Problem 138

A ladder leans against a building. The base of the ladder is 8 feet away from the wall of the building and reaches a height of 18 feet. Determine the angle, to the nearest degree, that the wall makes with the ladder.

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Problem 139

Find the exact solution of each xx for each inverse equation. a. 2cos1x=π2 \cos ^{-1} x=\pi b. 3tan1x=π3 \tan ^{-1} x=\pi

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Problem 140

Find secθ\sec \theta and cscθ\csc \theta if cotθ=1235\cot \theta=-\frac{12}{35} and cosθ<0\cos \theta<0.

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Problem 141

cosθ=22\cos \theta=-\frac{\sqrt{2}}{2}
Find all the solutions to cosθ=22\cos \theta=-\frac{\sqrt{2}}{2} in [0,2π)[0,2 \pi). θ=3π4,5π4\theta=\frac{3 \pi}{4}, \frac{5 \pi}{4} (Simplify your answer. Type an exact answer, using π\pi as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)
Write the general formula for all the solutions to cosθ=22\cos \theta=-\frac{\sqrt{2}}{2} based on the smaller angle. (Simplify your answer. Use angle measures greater than or equal to 0 and less than 2π2 \pi. Type an exact answer, using π\pi as needed. Use integers or fractions for any numbers in the expression. Type an expression using kk as the variable.)

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Problem 142

4. Below is a right-angled triangle.
Use trigonometry to work out the length x .

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Problem 143

Use a calculator to solve the equation on the interval 0θ<2π0 \leq \theta<2 \pi. 10cosθ3=010 \cos \theta-3=0 on 8 (0/1) on 12 (0/1) on 16 (0/1)
What are the solutions in the interval 0θ<2π0 \leq \theta<2 \pi ? Select the correct choice and fill in any answer boxes in your choice below. A. The solution set is \square }\} (Type your answer in radians. Round to two decimal places as needed. Us a comma to separate answers as needed.) B. There is no solution.

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Problem 144

cotxsecx=2cotx\cot x \sec x=\sqrt{2} \cot x for 0<x<2π0<x<2 \pi

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Problem 145

Verify that the equation given below is an identity. (Hint: cos2x=cos(x+x)\boldsymbol{\operatorname { c o s }} 2 x=\cos (x+x).) cos2x=cos2xsin2x\cos 2 x=\cos ^{2} x-\sin ^{2} x
Rewrite the expression on the left to put it in a more useful form cos2x=cos2x=cos2x=cos(xx)sin(π2x)cos(x+x)1sin2xcos2x\begin{array}{l} \cos 2 \mathrm{x}= \\ \cos 2 \mathrm{x}= \\ \cos 2 x= \\ \cos (x-x) \\ \sin (\pi-2 x) \\ \boldsymbol{\operatorname { c o s }}(\mathrm{x}+\mathrm{x}) \\ 1-\sin 2 x \\ -\cos 2 x \end{array}

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Problem 146

7. Algebraically find the solutions to the following trigonometric equations. Give solutions as exact values. a) cot2A+cotA=0\cot ^{2} A+\cot A=0 where πAπ-\pi \leq A \leq \pi b) 2cos2x=3cosx2 \cos ^{2} x=\sqrt{3} \cos x where 2πx0-2 \pi \leq x \leq 0

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Problem 147

4 Formula 2 points A force of magnitude 40 is applied to an object at angle 17 above horizontal as shown below. What is the xx-component of force Fin newtons? Enter only a numb in the blank. Round your answer to the nearest tenth (i.e. one decimal place).
Type your answer...

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Problem 148

4. San Francisco has some pretty steep streets. Some of which have inclines of 2525^{\circ}. a. Draw a force diagram and obtain the ΣF\Sigma \mathrm{F} equations for a car on such an incline. b. What static coefficient of friction is needed to prevent a car from sliding downhill? FFSF\mathrm{FFS}_{\mathrm{F}}

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Problem 149

7. Determine exact solutions for each equation in the interval x[0,2π]x \in[0,2 \pi]. a) sin2x14=0\sin ^{2} x-\frac{1}{4}=0 b) cos2x34=0\cos ^{2} x-\frac{3}{4}=0 c) tan2x3=0\tan ^{2} x-3=0 d) 3csc2x4=03 \csc ^{2} x-4=0 5.4 Solve Trigonometric Equations \cdot MHR 287

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Problem 150

Simplify the trigonometric expression. 1+sin(y)1+csc(y)\frac{1+\sin (y)}{1+\csc (y)}

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Problem 151

Verify the identity. csc(x)cos2(x)+sin(x)=csc(x)csc(x)cos2(x)+sin(x)=sin(x)+sin2(x)sin(x)=1=csc(x)\begin{aligned} \csc (x) \cos ^{2}(x) & +\sin (x)=\csc (x) \\ \csc (x) \cos ^{2}(x)+\sin (x) & =\frac{\square}{\sin (x)}+\frac{\sin ^{2}(x)}{\sin (x)} \\ & =\frac{1}{\square} \\ & =\csc (x) \end{aligned}

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Problem 152

Content attribution
QUESTION 4 - 1 POINT If angle A=31π18A=-\frac{31 \pi}{18} in radians, what is the degree measure of AA ?
Provide your answer below:

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Problem 153

Q9.
The graph shows the time of sunset (GMT) x days after the spring equinox (Mar 212024)
Its equation is t=6+2sin(2πx365)t=6+2 \sin \left(\frac{2 \pi x}{365}\right) a) Find the time of sunset 1 month ( 31 days) after the equinox (1) b) Find the maximum value of tt and the value of xx when tt reaches its maximum (2) c) Find the first two days when sunset is at 5 pm (4) d) Point A has coordinates (d,6)(\mathrm{d}, 6). State the value of d and the date it represents (2)

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Problem 154

If sint=1019\sin t=-\frac{10}{19} and if the terminal point is in Quadrant III, find tsint+sectt \sin t+\sec t

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Problem 155

Simplify csc2(t)1csc2(t)\frac{\csc ^{2}(t)-1}{\csc ^{2}(t)} to an expression involving a single trig function with no fractions. If needed, enter squared trigonometric expressions using the following notation. Example: Enter sin2(t)\sin ^{2}(t) as (sin(t))2(\sin (t))^{2}. \square

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Problem 156

From the information given, find the quadrant in which the terminal point determined by tt lies. Input I, II, III, or IV. (a) sin(t)<0\sin (t)<0 and cos(t)<0\cos (t)<0, quadrant (b) sin(t)>0\sin (t)>0 and cos(t)<0\cos (t)<0, quadrant (c) sin(t)>0\sin (t)>0 and cos(t)>0\cos (t)>0, quadrant (d) sin(t)<0\sin (t)<0 and cos(t)>0\cos (t)>0, quadrant

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Problem 157

Find the exact value of the expression. tan(sin1(23)cos1(15))\tan \left(\sin ^{-1}\left(\frac{2}{3}\right)-\cos ^{-1}\left(\frac{1}{5}\right)\right)

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Problem 158

Find all solutions of the given equation. (Enter your answers as a comma-separated list. Let kk be any integer. Do not round coefficients of kk. Other terms can be rounded to two decimal places where appropriate.) 2cos(θ)3=0θ=rad\begin{array}{r} 2 \cos (\theta)-\sqrt{3}=0 \\ \theta=\square \mathrm{rad} \end{array}

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Problem 159

If cotθ=15\cot \theta=-\frac{1}{5} and 3π2<θ<2π\frac{3 \pi}{2}<\theta<2 \pi, find cscθ\csc \theta cscθ=\csc \theta=

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Problem 160

Evaluate (if possible) the sine, cosine, and tangent at the real number tt. (If an answer is undetined, t=π3t=\frac{\pi}{3} sint=\sin t= \square cost=\cos t= \square tant=\tan t= \square

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Problem 161

la foncthon \rightarrow \rightarrow (axtb) Est perriodicgre de pariodie Tla.
Defermiter diors la perionte de chacuns des fonctions suivantes: f(x)=cos(2x+1);g(x)=tg(3x+2);f(x)=Sin(x+1)+Cos(13x+5)f(x)=\cos (2 x+1) ; g(x)=\operatorname{tg}(-3 x+2) ; \quad f(x)=\operatorname{Sin}(x+1)+\operatorname{Cos}\left(\frac{1}{3} x+5\right)

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Problem 162

If 0<x<π20<x<\frac{\pi}{2} then 1) 2π>sinxx\frac{2}{\pi}>\frac{\sin x}{x} 2) 2π<sinxx\frac{2}{\pi}<\frac{\sin x}{x} 3) sinxx>1\frac{\sin x}{x}>1 4) 2<sinxx2<\frac{\sin x}{x}

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Problem 163

1.) Graph y=sinθy=\sin \theta for the interval [2π,2π[-2 \pi, 2 \pi

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Problem 164

33
Тип 13 № 660752 i а) Решите уравнение cos2x3cos(xπ)undefinedcos(π+x)+1=cosx\cos 2 x-\sqrt{3} \underbrace{\cos (x-\pi)}_{\cos (-\pi+\mathrm{x})}+1=-\cos \mathrm{x}. б) Найдите все корни этого уравнения, принадлежащие отрезку [3π2;3π]\left[\frac{3 \pi}{2} ; 3 \pi\right].

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Problem 165

secθsinθtanθ+cotθ=sin2θ\frac{\sec \theta \sin \theta}{\tan \theta+\cot \theta}=\sin ^{2} \theta

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Problem 166

Score: 7/10 Penalty: none
Question Watch Video
The unit circle below shows 155155^{\circ} and 155-155^{\circ}. Find the values below, rounded to three decim necessary. tan(155)=tan(155)=tan(155)=tan(155)\begin{array}{l} \tan \left(155^{\circ}\right)=\square \\ \tan \left(-155^{\circ}\right)=\square \\ \tan \left(155^{\circ}\right)=-\tan \left(-155^{\circ}\right) \end{array}

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Problem 167

Find the exact value of sinπ4\sin \frac{\pi}{4} in simplest form with a rational denominator.
Answer

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Problem 168

Use your calculator to evaluate each expression. Give answers in degrees, rounded to 1 decimal place. sin1(0.25)=cos1(0.48)=tan1(6)=\begin{array}{l} \sin ^{-1}(-0.25)=\square \\ \cos ^{-1}(0.48)=\square \\ \tan ^{-1}(6)=\square \end{array}
Try reloading this question and estimating the answers in your head before using a calcula Submit Question

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Problem 169

Suppose x=4x=4 and y=7y=7 in the figure, which is not drawn to scale. Find the following. Enter exact answers given as fractions, not decimal approximations. help (fractions)
1. cos(θ)=\cos (\theta)= \square
2. sin(θ)=\sin (\theta)= \square
3. tan(θ)=\tan (\theta)= \square

Note: You can earn partial credit on this problem.

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Problem 170

Evaluate the following expressions. Your answer must be an angle in radians and in the interval [π2,π2]\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]. (a) sin1(0)=\sin ^{-1}(0)= \square (b) sin1(22)=\sin ^{-1}\left(\frac{\sqrt{2}}{2}\right)= \square (c) sin1(32)=\sin ^{-1}\left(\frac{\sqrt{3}}{2}\right)= \square Submit Question

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Problem 171

Question 1 of 3, Step 2 of 2 TRINITEE NEWMAN 8/6 Correct
Graph the following function: y=352cot(x)y=3-\frac{5}{2} \cot (x)
Step 2 of 2: Determine how the general shape of the graph, chosen in the previous step, would be shifted, stretched, and reflected for the given function. Graph the results on the axes provided.
Answer Keypac Keyboard Shortch xx-Axis Reflection nenect graph across xx-axis
Shift Graph Vertically UpU_{p} Down None Shift Graph Horizontally (Phase Shift) Left Right None
Stretch/Compress Graph Vertically Yes No
Stretch/Compress Graph Horizontally (Period) Yes No Enable Zoom/Pan Submit Answer - 2024 Hawkes Learning D=14D=14

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Problem 172

Exercises compute sinθ\sin \theta and cosθ\cos \theta for θ=15\theta=15^{\circ} and 7575^{\circ} respectively

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Problem 173

31 Tun 13 No 500212i500212 i а) Решите уравнение 6sin2x+5sin(π2x)2=06 \sin ^{2} x+5 \sin \left(\frac{\pi}{2}-x\right)-2=0. 6) Найдите все кории этого уравиеиия, приндлежашие огрезку [5π,7π2]\left[-5 \pi,-\frac{7 \pi}{2}\right].

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Problem 174

What is the value of xx in the triangle? 8.12 cm 7.73 cm 16.5 cm 23.78 cm

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Problem 175

Find all solutions to each equation in radians. 4+15sec(2θ+2π3)=83+4+3sec(2θ+2π3)4+15 \sec \left(-2 \theta+\frac{2 \pi}{3}\right)=8 \sqrt{3}+4+3 \sec \left(-2 \theta+\frac{2 \pi}{3}\right) A) {3π+6πn,π4πn}\left\{3 \pi+6 \pi n, \frac{\pi}{4}-\pi n\right\} B) {7π12πn,π4πn}\left\{-\frac{7 \pi}{12}-\pi n, \frac{\pi}{4}-\pi n\right\} C) {3π+6πn}\{3 \pi+6 \pi n\} D) {7π12πn,3π+6πn}\left\{-\frac{7 \pi}{12}-\pi n, 3 \pi+6 \pi n\right\}

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Problem 176

Evaluate using a calculator. Be sure the calculator is in the correct mode. sin43sin43=\begin{array}{l} \sin 43^{\circ} \\ \sin 43^{\circ}= \end{array} \square (Round to three decimal places.)

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Problem 177

Convert each degree measure into radians and each radian measure into degrees. 31π6\frac{31 \pi}{6} A) 19201920^{\circ} B) 930930^{\circ} C) 800800^{\circ} D) 890890^{\circ}

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Problem 178

19. Given the function below, find the 5 points amplitude. (The same function will be used for problems 19-22). y=2sin(4xπ4)+5y=2 \sin \left(4 x-\frac{\pi}{4}\right)+5 A. Amp. =5=5 B. Amp. =4=4 C. Amp. =2=2 D. Amp. =π4=\frac{\pi}{4} AA B C D

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Problem 179

Find the reference angle. 575575^{\circ} A) 55^{\circ} B) 3535^{\circ} C) 7070^{\circ} D) 5555^{\circ}

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Problem 180

Find the measure of each angle. A) 2π-2 \pi B) 4π4 \pi C) 7π2-\frac{7 \pi}{2} D) 5π4-\frac{5 \pi}{4}

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Problem 181

c 3sin2xcos2x=03 \sin 2 x-\cos 2 x=0

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Problem 182

Find the reference angle. A) 11π36\frac{11 \pi}{36} B) π9\frac{\pi}{9} C) 5π18\frac{5 \pi}{18} D) 2π9\frac{2 \pi}{9}

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Problem 183

Solve the equation on the interval 0x2π0 \leq x \leq 2 \pi a. 4sinθ+33=34 \sin \theta+3 \sqrt{3}=\sqrt{3}

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Problem 184

11sin2x=1+tan2x\frac{1}{1-\sin ^{2} x}=1+\tan ^{2} x

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Problem 185

(3) 3sin2x=2tg2x3 \sin 2 x=2 \operatorname{tg} 2 x

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Problem 186

f. (tanθ1)(secθ1)=0(\tan \theta-1)(\sec \theta-1)=0

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Problem 187

c. cos2θsin2θ+sinθ=0\cos ^{2} \theta-\sin ^{2} \theta+\sin \theta=0

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Problem 188

Use the half-angle formula to find the exact value of cos(15)=\cos \left(15^{\circ}\right)= \square
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Problem 189

3) Dado cosα=32\cos \alpha=\frac{\sqrt{3}}{2}, calcular Sen 2α,Cos2α,Tg2α2 \alpha, \operatorname{Cos} 2 \alpha, \operatorname{Tg} 2 \alpha

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Problem 190

Find all xx in the interval [0,2π)[0,2 \pi) such that cosx=0.9213\cos x=-0.9213 :

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Problem 191

Write down the three forms of the double-angle formula for cosine:

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Problem 192

30. cosx1sinx=secx+tanx\frac{\cos x}{1-\sin x}=\sec x+\tan x

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Problem 193

Solve the equation. Give all solution in 0θ<2π0 \leq \theta<2 \pi 2cos(θ)=12 \cos (\theta)=1
Select all that apply 0 π2\frac{\pi}{2} π\pi 3π2\frac{3 \pi}{2} π6-\frac{\pi}{6} π6\frac{\pi}{6} 2π3\frac{2 \pi}{3} 7π6\frac{7 \pi}{6} 5π3\frac{5 \pi}{3} π4-\frac{\pi}{4} π4\frac{\pi}{4} 3π4\frac{3 \pi}{4} 5π4\frac{5 \pi}{4} 7π4\frac{7 \pi}{4} π3-\frac{\pi}{3} π3\frac{\pi}{3} 5π6\frac{5 \pi}{6} 4π3\frac{4 \pi}{3} 11π6\frac{11 \pi}{6} π2-\frac{\pi}{2}

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Problem 194

 o|e్1 A| \begin{array}{l} \text { o|e్1 A| } \end{array} \begin{array}{l} \Rightarrow \end{array} \square\square \square \square \square \square \square 0 0 \vdots \vdots Δ\Delta

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Problem 195

2) Determine the exact value: (6 marks) csc240\csc 240^{\circ} cot120\cot 120^{\circ}

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Problem 196

4) Prove Trigonometric Identities tanθ+cotθ=secθcscθ\tan \theta+\cot \theta=\sec \theta \csc \theta

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Problem 197

Given secA=857\sec A=-\frac{\sqrt{85}}{7} and that angle AA is in Quadrant II, find the exact value of cscA\csc A in simplest radical form using a rational denominator.

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Problem 198

can2α1+can2α=sin2α\frac{\operatorname{can}^{2} \alpha}{1+\operatorname{can}^{2} \alpha}=\sin ^{2} \alpha

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Problem 199

4) Prove Trigonometric Identities (10 marks, 5 each) tanθ+cotθ=secθcscθcan2α1+can2α=sin2α\tan \theta+\cot \theta=\sec \theta \csc \theta \quad \frac{\operatorname{can}^{2} \alpha}{1+\operatorname{can}^{2} \alpha}=\sin ^{2} \alpha

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Problem 200

6) (7 marks) In ABC\triangle A B C, determine A\angle A to the nearest degree if a=55 cm;b=26 cma=55 \mathrm{~cm} ; b=26 \mathrm{~cm}, and c=32 cmc=32 \mathrm{~cm}.

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